Synchronization and implementation of adaptive observer based hyperchaotic systems

Chaos in the nonlinear sciences has witnessed an increase in research activity since the 1990s. Extensive studies have been conducted on the rich and complex dynamics of chaos, along with its potential applications. It is particularly noteworthy that various encryption schemes based on synchronization have been proposed as a result of the special characteristics of chaotic systems. During this period, the exploration of the intricate dynamics of chaotic systems has significantly advanced the understanding and applicability of chaos in the scientific community. In particular, the unpredictability of chaos, stemming from the sensitivity to small initial conditions in deterministic systems, holds great importance in the design and implementation of secure communication systems. This thesis explores the synchronization and implementation of adaptive observer-based hyperchaotic systems. Hyperchaotic systems, characterized by a larger number of positive Lyapunov exponents compared to chaotic systems, pose unique challenges and opportunities in control and synchronization. In this study, two distinct hyperchaotic systems are introduced. The dynamical properties and phase space analysis of these proposed hyperchaotic systems have been thoroughly investigated. Furthermore, a circuit simulation of one of the proposed hyperchaotic systems has been developed. Synchronization has been successfully achieved for both hyperchaotic systems. The first hyperchaotic system is employed for adaptive synchronization using specialized control strategies, while the second hyperchaotic system serves as a reference for adaptive observer synchronization. In this approach, an observer-based technique is applied to synchronize its dynamics with another system. These implemented synchronization methods are subsequently applied to secure communication applications. The simulation results substantiate the effectiveness of the approach by demonstrating successful outcomes in both adaptive synchronization and adaptive observer-based synchronization scenarios. Furthermore, the performance observed in secure communication applications attests to the efficacy of the designed synchronizations. These findings not only contribute to the theoretical understanding of hyperchaotic systems but also offer practical insights into the application of synchronization techniques. This research contributes to the advancement of chaos control by presenting an approach to hyperchaotic system synchronization and addressing the complexities inherent in the implementation of adaptive synchronization and adaptive observer-based methodologies. Keywords: Hyperchaotic Systems, Synchronization, Circuit Implementation, Adaptive Observer